U.S. patent application number 11/284331 was filed with the patent office on 2006-06-22 for positioning system.
Invention is credited to Dirk Verdyck, Bart Verhoest.
Application Number | 20060132529 11/284331 |
Document ID | / |
Family ID | 36595105 |
Filed Date | 2006-06-22 |
United States Patent
Application |
20060132529 |
Kind Code |
A1 |
Verhoest; Bart ; et
al. |
June 22, 2006 |
Positioning system
Abstract
A positioning system includes adjustment means for accurately
positioning a positioning device relative to a frame. The
adjustment means makes a sliding contact with a dedicated lever
which makes contact with the frame. The contact surfaces of the
dedicated lever are specially shaped in order to obtain a linear
behavior of the positioning system. Within a working distance D an
equal movement of the adjustment means over a distance .DELTA.x is
converted into a corresponding movement of the positioning device
relative to the frame over a distance .DELTA.y. The ratio
.DELTA.x/.DELTA.y is substantially constant for movements within
the working distance D. When using the positioning system in a
printing system, it is possible to measure the position error of
printheads having arrays of printing elements only once and adjust
the positioning devices carrying the printheads only once to align
the printing elements to each other and to the printing direction
of the printer.
Inventors: |
Verhoest; Bart; (Niel,
BE) ; Verdyck; Dirk; (Merksem, BE) |
Correspondence
Address: |
AGFA CORPORATION;LAW & PATENT DEPARTMENT
200 BALLARDVALE STREET
WILMINGTON
MA
01887
US
|
Family ID: |
36595105 |
Appl. No.: |
11/284331 |
Filed: |
November 21, 2005 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60648022 |
Mar 4, 2005 |
|
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Current U.S.
Class: |
347/19 |
Current CPC
Class: |
B41J 25/003 20130101;
B41J 25/001 20130101 |
Class at
Publication: |
347/019 |
International
Class: |
B41J 29/393 20060101
B41J029/393 |
Foreign Application Data
Date |
Code |
Application Number |
Dec 22, 2004 |
EP |
04106837.0 |
Jun 7, 2005 |
EP |
05104914.6 |
Claims
1. A positioning system for accurately positioning an element
relative to a frame comprising: a positioning device, adjustably
mounted on said frame or carrying said element mounted in the
positioning device, an adjustment means, adjustable over a working
distance D for setting the position of the positioning device
relative to the frame and making a first sliding butting contact to
a lever making a second sliding butting contact to the positioning
device on the frame or frame itself for transferring movement of
the adjustment means over a distance .DELTA.x into a corresponding
movement of the positioning device relative to the frame over a
distance .DELTA.y, characterized in that ratio .DELTA.x/.DELTA.y is
substantially constant for movements within the working distance
D.
2. The positioning system according to claim 1 wherein the forces
acting upon the lever by the adjustment means and by the
positioning device are always perpendicular to the butting surface
of the lever.
3. The positioning system according to claim 1 wherein the ratio of
the length of the load arm to the length of the force arm of the
lever is constant.
4. The positioning system to claim 1 wherein the butting surfaces
of the lever are formed by the union of contact points defined by
the solution of the boundary value problem: { 0 = sin .times.
.times. .theta. + cos .times. .times. .theta. d y d x .times.
.times. or .times. .times. d y d x = - tan .times. .times. .theta.
d .theta. d x = 1 cos .times. .times. .theta. .function. ( x 1
.times. d f d .theta. + x .times. .times. sin .times. .times.
.theta. + y .times. .times. cos .times. .times. .theta. ) ##EQU40##
wherein .DELTA.x is a linear function of .DELTA.y and wherein
x=value of a boundary point along the abscissa. .theta.=angle
position of the lever y=coordinate describing shape of the lever as
function of the local coordinate x.
5. The positioning system according to claim 4 wherein the working
distance D is situated in between singular working points of the
lever mechanism.
6. The positioning system according to claim 1 wherein the angle
between the contact points of the load arm, the rotation point and
the contact point of the force arm is constant.
7. The positioning system according to claim 1 wherein the
adjustment means and rotation point of the lever are mounted on the
positioning device and the second butting contact is in contact
with the frame.
8. The positioning system according to claim 1 wherein a resilient
means urges the positioning device on the frame or the frame itself
in contact with the lever.
9. The positioning system according to claim 1 wherein the element
mounted on the positioning device is a printhead.
10. An inkjet printer comprising at least one printhead mounted on
a positioning system according to claim 1.
Description
[0001] The application claims the benefit of U.S. Provisional
Application No. 60/648,022 filed Mar. 4, 2005.
[0002] The present invention relates to a positioning system for
positioning an element relative to a frame. More specifically a
positioning system which can be used in a dot matrix printing
system for positioning printheads relative to a mounting frame or
base plate and to each other.
BACKGROUND OF THE INVENTION
[0003] When using a printing technique that puts down marking
material, e.g. ink, on a receiving substrate in a matrix form, the
image to be produced is rendered before it is printed. Rendering
creates a representation of the image as a matrix of individual
marking points in such a way that printing the individual marking
point at their correct matrix position resembles the original image
as close as possible. In the final printed image the position of
the individual marking points is crucial to the quality of the
image. Any errors in the position of the printed marking points on
the receiving substrate from their position assumed in the
rendering process, shows up in the printed image. Marking points
being too close to each other show macroscopically as an area that
has received too much marking material than it should have; marking
points being too far separated show macroscopically as an area that
has received too little marking material than it should have. When
positional errors become systematic, they can show as stripes in
the printed image. Of primary importance in controlling the
position where the marking material is printed, is the position of
the printing head providing the marking material via a plurality of
marking elements. In scanning printing systems, color printing
systems or printing systems using butted heads, the printing heads
needs to be positioned and aligned correctly with respect to each
other and with respect to the receiving substrate. This to ensure a
correct superposition of the color separated images and good
fitting of the image bands printed by each printhead.
[0004] In patent application WO 01/60 627 from Xaar, herein
incorporated by reference in its entirety for background
information only, the printing heads are adjustably mounted on a
single base plate. The position of each printing head can be
adjusted with reference to a datum on the base plate. All printing
heads are positioned with reference to the same datum so that they
can all be aligned properly. The base plate itself is positioned
against datums on the printer body so that finally the position of
the marking elements of the printing heads relative to the printer
body is known at all times. The positioning of printing heads
relative to datums fixed on a carriage or printer body is commonly
known.
[0005] In patent application WO 01/60 627 the alignment is done via
specially shaped screws that drive the printing heads against
specially shaped features on the base plate.
[0006] Aligning the printing heads is an iterative process because
it required a test print after each screw adjustment to see the
effect of the adjustment on the print result. This needs to be
repeated until perfect alignment is achieved. Therefore the
alignment of printing heads after printer installation or after
printing head replacement is a tedious work and is often performed
by the printer manufacturer or install/service team, but seldom by
the printer operator.
[0007] Printhead mounting systems sometimes include a printhead
holding device which is rigidly mounted on a base plate and wherein
a printhead is adjustably mounted. The printhead has to be clamped
in a secure way in the printhead holding device while at the same
time the printhead itself should be accurately positionable within
the device. These goals are not always compatible to each
other.
[0008] Positioning screws are sometimes hardly accessible as these
are mounted close to the base plate. This provides further
difficulties in the tedious adjustment of the printheads. Certain
inkjet printing systems include up to eight different printheads in
a small space and aligning the different heads in the three
dimensions requires a considerable effort.
[0009] Another problem is that forces acting on the adjustment
screws can include a transversal component, i.e. the screw is not
only pushed upwards but also sideways due to an oblique butting
contact to a surface.
[0010] Relative large sideways forces can act on the screws.
Especially for a high precision alignment system this should be
avoided as this can lead to premature wear leading to play in the
system resulting in inaccurate positioning.
[0011] It is clear that there is a need for a cheap, easy and
reliable positioning system for positioning e.g. used for
positioning a printhead. When adjustments are made the displacement
should be predictable, so that deviation of the printheads only
needs to be measured and adjusted once. The design should have a
inherent property that transversal forces are avoided.
SUMMARY OF THE INVENTION
[0012] The above-mentioned advantageous effects are realized by a
positioning system having the specific features set out in claim 1.
Specific features for preferred embodiments of the invention are
set out in the dependent claims.
[0013] Further advantages and embodiments of the present invention
will become apparent from the following description and
drawings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0014] FIGS. 1A, 1B, 1C show the behavior of an ideal lever.
[0015] FIGS. 2A and 2B illustrate the existence of a singular
point.
[0016] FIGS. 3A and 3B illustrate the migration of the contact
point on the force arm of the lever.
[0017] FIGS. 4A and 4B illustrate the migration of the contact
point on the load arm of the lever.
[0018] FIGS. 5A and 5B illustrate the contact point migration when
using a segment of a circle as contact area on the lever.
[0019] FIG. 6 depicts a general case of a solid body defined by
boundary function in a certain rotational position .theta..
[0020] FIGS. 7A and 7B give the ideal forms of the contact surfaces
of the lever according to an embodiment of the present invention
wherein the contact points remain at fixed positions.
[0021] FIG. 8 gives the deviation from linearity of a lever
according to the present invention.
[0022] FIG. 9 gives the deviation from linearity of the lever using
segments of a circle as contact surface.
[0023] FIGS. 10A and 10B give the ideal forms of the contact
surfaces of the lever according to an embodiment of the present
invention with moving contact points.
[0024] FIG. 11 gives an printhead holding device using a position
system according to the present invention.
[0025] FIG. 12 illustrates that by translation of the marking
elements due to rotation of the head positioning device can be
avoided by having the rotation point slide along the x-axis.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0026] While the present invention will hereinafter be described in
connection with preferred embodiments thereof, it will be
understood that it is not intended to limit the invention to those
embodiments.
[0027] The invention provides a positioning system that allows for
mounting an element in a positioning device which can be accurately
positioned relative to a frame carrying the positioning device,
e.g. the printing head in a printing apparatus is mounted in a
printhead positioning device which can be accurately aligned to a
base plate carrying the positioning device. The positioning system
according to the invention also avoids exerting excessive lateral
forces onto the adjustment elements.
[0028] The positioning system provides a proportional relationship
between a displacement of the adjustment means, easily accessible
to the operator, and the movement in the position of the
positioning device relative to the frame.
[0029] Due to a proportional relationship between the movement
.DELTA.x of the adjusting means and the displacement .DELTA.y of
the positioning device, a reliable, accurate and predictable
adjustment can be performed. Once an alignment error is known, a
single adjustment can give a perfect alignment.
[0030] The proportional relationship is guaranteed by a dedicated
lever mechanism meeting a number of geometric constraints with
respect to the shape of the lever, especially the contact surfaces
on which the forces on the lever act, and the orientation of the
interface surface between lever and acting force and base plate.
Using the dedicated lever mechanism a rotation of an adjustment
screw on the head positioning device is transformed into a linear
displacement of the positioning device relative to a mounting base
plate. The adjustment means are self-locking and have no backlash,
securing the position of the printing head at all times.
Considerations Regarding the Working Conditions of a Lever
[0031] Let us consider an ideal lever, as shown in FIG. 1A, which
could be used in a positioning system for positioning an
positioning device relatively to a frame.
[0032] The lever 1 has a rotation point 2 which is a fixed point on
the frame (or on the element to be positioned relatively to the
frame), a force arm 3 at which force is exerted by an adjustment
means 4 and a load arm 5 butting against the load 6 (element or the
frame.)
[0033] As the lever is an ideal lever: [0034] the contacts of the
lever 1 with the adjustment means 4 and the load 6 are ideal point
contacts; and [0035] the surfaces of the force and load arms 3,5
are perfectly flat surfaces.
[0036] The forces of the adjustment means 4 and the load 6 are at
the same angle relatively to the force and load arm 3,5.
[0037] A further restraint in the system is that the orientation of
the adjustment means 4 and force of the load 6 is fixed. A
practical design of the adjustment means 4 is the use of a screw
which can regulate the height of the force lever 3. The load 6 can
be an element to be positioned and which can slide along a rail
mounted on the frame. Practical examples are given further
below.
[0038] Referring to FIG. 1A, when the adjustment means 4 is
adjusted over a distance .DELTA.x, the lever will rotate over an
angle .theta. which is dependent upon the length Lf of the force
arm. A force arm is defined as the perpendicular distance from the
force to the rotation point. Equation .times. .times. 1 .times. :
##EQU1## .theta. = arc .times. .times. Tg .times. .DELTA. .times.
.times. x Lf ##EQU1.2##
[0039] The rotation .theta. causes a displacement .DELTA.y of the
load which is dependant upon the length or the load arm. Equation
.times. .times. 2 .times. : ##EQU2## .theta. = arc .times. .times.
Tg .times. .DELTA. .times. .times. y Ll ##EQU2.2##
[0040] And hence .DELTA.x/.DELTA.y=Lf/Ll which could be expected.
The ratio of the displacement values depends on the ratio of the
length of the force and load arms.
[0041] However, because the orientation and place of the adjustment
means and load are fixed a consequence is that the length of the
force and load arm will not change during the rotation, as the
force arm is the perpendicular distance of the force to the
rotation point. From FIG. 1B it can be seen that the force lever
arm length will grow longer to value Lf' and the load lever arm
length will grow longer to Ll', wherein Lf'=Lf/cos .theta. and
Ll'=Ll/cos .theta.. The ratio of the lengths of the force (Lf) and
load arm (Ll) will not change in these ideal conditions. Equation
.times. .times. 3 .times. : ##EQU3## Lf Ll == Lf ' cos .times.
.times. .theta. Ll ' cos .times. .times. .theta. = Lf ' Ll '
##EQU3.2##
[0042] The displacement .DELTA.x of the adjustment device will
always result in the same correcponding movement .DELTA.y.
[0043] If we take the more general case, as depicted in FIG. 1c,
then we can try to write the exact relationship between .DELTA.x
and .DELTA.y for a given rotation .DELTA..theta. of the object.
Consider a displacement of the first point at force lever from
.theta..sub.1 to .theta..sub.1+.DELTA..theta.. Due to the fact that
we keep the force arm constant during this movement, we can write:
Equation .times. .times. 4 .times. : ##EQU4## { Lf .times. .times.
cos .times. .times. .theta. = ( Lf + .DELTA. .times. .times. Lf )
.times. cos .function. ( .theta. f + .DELTA..theta. ) Lf .times.
.times. sin .times. .times. .theta. f = ( Lf + .DELTA. .times.
.times. Lf ) .times. sin .function. ( .theta. f + .DELTA..theta. )
+ .DELTA.y . ##EQU4.2##
[0044] From this equation, the term Lf-.DELTA.Lf can be removed so
that we end up with a relationship between .DELTA.y as a function
of .DELTA..theta.: Equation .times. .times. 5 .times. : ##EQU5##
.DELTA. .times. .times. y = Lf .times. sin .times. .times.
.DELTA..theta. cos .function. ( .theta. f + .DELTA..theta. ) .
##EQU5.2##
[0045] A similar equation can be found for .DELTA.x: Equation
.times. .times. 6 .times. : ##EQU6## .DELTA. .times. .times. x = Ll
.times. sin .times. .times. .DELTA..theta. cos .function. ( .theta.
l + .DELTA..theta. ) . ##EQU6.2##
[0046] We can then write the ratio of .DELTA.x/.DELTA.y for a
straight contact surface as: Equation .times. .times. 7 .times. :
##EQU7## .DELTA. .times. .times. x .DELTA. .times. .times. y = Ll
Lf cos .function. ( .theta. f + .DELTA..theta. ) cos .function. (
.theta. l + .DELTA..theta. ) . ##EQU7.2##
[0047] So, in order to have the ratio of .DELTA.x to .DELTA.y
constant, for random values of .theta..sub.f and .theta..sub.1,
this is only possible when of equals .theta..sub.1, or when the two
lever arms are positioned relative to each other with a right
angle. But we need another mandatory constraint and that is the
fact that the forces should be perpendicular to the contact surface
of the lever, which in practice will give a surface trajectory that
is rather complex in order to fulfil both conditions. Therefore, in
practice, due to the complex nature of these surfaces, the
adjustment range of the adjustment means is to be restricted to a
certain distance X as lever arms would become extremely long at
great rotation angles.
[0048] Several problems can be encountered in reality when the
lever is not the mathematical ideal lever.
Occurrence of Singular Points in the Operating Interval
[0049] Under certain conditions the ratio of the force and load arm
will change during rotation. Consider the situation depicted in
FIG. 2A. The force of the adjustment means is at a different angle
to the force arm than the angle of the load to the load arm.
[0050] During rotation, evaluating to the situation of FIG. 2B, it
can be clearly seen that length of the force arm Lf has become
shorter Lf' over the rotation angle .theta. while the load arm Ll
has grown larger Ll' over the rotation .theta..
[0051] A constant value for the ratio of the evolving lever arm
lengths is clearly not satisfied in this example. A displacement of
the adjustment means over an equal distance .DELTA.x will not
result in a equal displacement .DELTA.y as the ratio of the force
and load arms.
[0052] When rotating further the force arm will become longer
again, but even if both arms grow longer the ratio of the force and
load arm will still vary as the cosine function is not a linear
function.
[0053] Another problem is that in a real situation the contact
between the lever arm and the adjustment device/load is not a point
contact. Clarification is given in relation to FIGS. 3A and 3B.
[0054] In FIG. 3A the contact of the regulating screw of the
adjustment device is depicted while being in contact with the
horizontal surface of the force arm of the lever. The contact point
can be defined at the center of the regulating screw at the
interface with the lever.
[0055] In FIG. 3B the situation is depicted while the lever force
arm is at an angle .theta.. It is clear that the contact point has
migrated a small distance in the direction of the rotation point of
the lever, so the length of the force arm is a bit shorter than
would be expected from the ideal situation as described above.
[0056] In 4A and 4B it can be seen that for the load arm the length
of the load arm tends to be a bit longer than expected due to the
rotation and the non-perfect contact.
[0057] Due to these imperfections the linear relationship between
.DELTA.x and .DELTA.y is disturbed. In a micropositioning system
such as used for positioning e.g. inkjet printhead this is not to
be neglected. The non-linearity makes it impossible to predictably
adjust the position of the element. Alignment without several newly
printed test images is impossible.
[0058] Another drawback is that after rotation of the lever over an
angle .theta. the forces acting upon the regulation screw are not
parallel to the center line of the screw. The butting pressure does
have a transversal component which is larger as the angle
increases.
[0059] This also leads to possible variations in the positioning
system and leads after time to play and imperfections in the
adjustment system. It is to be desired that the contact between
adjustment device/load and lever is to be close as possible to the
ideal point contact.
[0060] One method to obtain this point-like contact is by giving
the lever used in the positioning system a curved surface. A
possible solution shown in FIG. 5A is that the contact area of the
lever is a segment of a circle. Then the resulting contact is more
point-like but has another consequence.
[0061] Due to translation of the contact point over the curved
surface of the lever during rotation as shown in FIG. 5B, the ratio
of the length of the force arm and the length of the load arm can
be kept constant, but also the lever angle between the force arm
and load arm slightly changes as can be seen by the change of the
contact lines with angles .alpha. and .beta., also influencing the
relationship between .DELTA.x and .DELTA.y and making it
non-linear.
Design of Lever Arm Contact Surfaces for Linear Operation
[0062] A more fundamental approach can be taken to obtain a linear
relationship between .DELTA.x and .DELTA.y. Let's make a force
analysis on a structure and let us apply the principle of virtual
force. FIG. 6 gives the theoretical situation of a random structure
which is controlled by forces. Note that in FIG. 6 .DELTA.x is
associated with a displacement of the structure at the load
position t=t2 in horizontal direction and .DELTA.y is associated
with a displacement of the structure at the force position t=t1 in
vertical direction, contrary to the use of .DELTA.x and .DELTA.y in
the previous figures.
[0063] In a stationary situation, the forces acting on the
structure should balance each other. Assuming that no torque is
possible in the origin (0,0), the moment equation of the body gives
the equation 8. AF.sub.1=BF.sub.2[Nm] Equation 8
[0064] Suppose that in contact point t=t1, a small movement
.DELTA.y1 is given, which will result in a movement .DELTA.x2 in
contact point t=t2. Due to the principle of virtual work, the
delivered energy will stay constant.
F.sub.1.DELTA.y.sub.1=F.sub.2.DELTA.x.sub.2[J] Equation 9
[0065] For the above equation to be correct, it is mandatory that
both forces act on the surface in the same angle at the contact
point. Also, during the movement, it is assumed that no friction
force is present.
[0066] Substituting Equation 8 gives. Equation .times. .times. 10
.times. : ##EQU8## .DELTA. .times. .times. x 2 = B A .DELTA.
.times. .times. y 1 .times. [ m ] ##EQU8.2##
[0067] If the ratio of .DELTA.x.sub.2/.DELTA.y.sub.1 should stay
constant, it is mandatory to keep the ratio B/A constant. So, this
means that: [0068] A. we make the type of the contact points so
that they always stays at the distances A and B; [0069] Or [0070]
B. we make the type of the contact points so that they shift in
distance, but with a same ratio, meaning: Equation .times. .times.
11 .times. : ##EQU9## B A = Bf .function. ( .theta. ) Af .function.
( .theta. ) .times. [ ] , ##EQU9.2##
[0071] with f(.theta.) a continues function of .theta..
A. Kinematics for Contact Points Remaining at Fixed A and B
Positions, i.e. Having Only One Degree of Freedom
[0072] With continued reference to FIG. 6, imagine the random
structure or plane object having a boundary .GAMMA., where each
coordinate point of this boundary .GAMMA. can be described by the
following function: Equation .times. .times. 12 .times. : ##EQU10##
( x y ) .GAMMA. = ( .GAMMA. x .function. ( t ) .GAMMA. y .function.
( t ) ) ##EQU10.2##
[0073] The coordinate system has been taken in such a way that a
pivot point exists at the origin of the axis system. So, the point
(0,0) is a rotating point for the plane body and the rotational
position of the plane body can be described uniquely by an angle
.theta.. Assume also that the location of the boundary points in
Equation 12 are defined for the angle .theta. being identical to
zero. When .theta. is not zero, the coordinates of the boundary
points can be found by a simple rotational transformation: Equation
.times. .times. 13 .times. : ##EQU11## .times. ( x .function. ( t ,
.theta. ) y .function. ( t , .theta. ) ) .GAMMA. = ( cos .times.
.times. .theta. - sin .times. .times. .theta. sin .times. .times.
.theta. cos .times. .times. .theta. ) .times. ( .GAMMA. x
.function. ( t ) .GAMMA. y .function. ( t ) ) ##EQU11.2##
[0074] This can be written also as: Equation .times. .times. 14
.times. : ##EQU12## .times. { x .function. ( t , .theta. ) = cos
.times. .times. .theta. .GAMMA. x .function. ( t ) - sin .times.
.times. .theta. .GAMMA. y .function. ( t ) y .function. ( t ,
.theta. ) = sin .times. .times. .theta. .GAMMA. x .function. ( t )
+ cos .times. .times. .theta. .GAMMA. y .function. ( t ) .
##EQU12.2##
[0075] At a certain boundary point (x.sub.1,y.sub.1) that can be
found at the coordinate t.sub.1 in a certain random angle position
.theta., a displacement is given of the form: (0,.DELTA.y), imposed
by a thin rod, pushing against the boundary and also sliding in the
x-direction over this boundary. What will be the angle rotation
d.theta. of the plane object?
[0076] For an imposed displacement (0,.DELTA.y), the object will
rotate and the contact point will shift from the position t.sub.1
to a position t.sub.1+dt. Equation .times. .times. 15 .times. :
##EQU13## .times. { 0 = dx .function. ( t 1 , .theta. ) = - sin
.times. .times. .theta. .GAMMA. x .function. ( t 1 ) d .times.
.times. .theta. + cos .times. .times. .theta. .times. d .GAMMA. x
.function. ( t 1 ) d t .times. d .times. .times. t - cos .times.
.times. .theta. .GAMMA. y .function. ( t 1 ) .times. d .times.
.times. .theta. - sin .times. .times. .theta. .times. d .GAMMA. y
.function. ( t 1 ) d t .times. d .times. .times. t .DELTA. .times.
.times. y = dy .function. ( t 1 , .theta. ) = cos .times. .times.
.theta. .GAMMA. x .function. ( t 1 ) d .times. .times. .theta. +
sin .times. .times. .theta. .times. d .GAMMA. x .function. ( t 1 )
d t .times. d .times. .times. t - sin .times. .times. .theta.
.GAMMA. y .function. ( t 1 ) .times. d .times. .times. .theta. +
cos .times. .times. .theta. .times. d .GAMMA. y .function. ( t 1 )
d t .times. d .times. .times. t ##EQU13.2##
[0077] From this system of equation, the rotation d.theta. of the
object can be solved by eliminating dt, as it is of no interest to
us. Equation .times. .times. 16 .times. : ##EQU14## .times. d
.times. .times. .theta. = .DELTA. .times. .times. y .times. .times.
cos .times. .times. .theta. .times. d .GAMMA. x .function. ( t 1 )
d t - sin .times. .times. .theta. .times. d .GAMMA. y .function. (
t 1 ) d t ( cos .times. .times. .theta. .GAMMA. x .function. ( t 1
) - sin .times. .times. .theta. .GAMMA. y .function. ( t 1 ) )
.times. ( cos .times. .times. .theta. .times. d .GAMMA. x
.function. ( t 1 ) d t - sin .times. .times. .theta. .times. d
.GAMMA. y .function. ( t 1 ) d t ) + ( sin .times. .times. .theta.
.GAMMA. x .function. ( t 1 ) + cos .times. .times. .theta. .GAMMA.
y .function. ( t 1 ) ) .times. ( sin .times. .times. .theta.
.times. d .GAMMA. x .function. ( t 1 ) d t + cos .times. .times.
.theta. .times. d .GAMMA. y .function. ( t 1 ) d t )
##EQU14.2##
[0078] Let's try this equation. We take a simple boundary, being a
straight line lying on the x-axis, so that the points of the
boundary described by Equation 12 can be written as: Equation
.times. .times. 17 .times. : ##EQU15## .times. ( x y ) .GAMMA. = (
.GAMMA. x .function. ( t ) .GAMMA. y .function. ( t ) ) = ( - t 0 )
##EQU15.2##
[0079] At t=t.sub.1, we give a displacement .DELTA.y. The expected
rotation d.theta. for .theta.=0 equals -.DELTA.y/t.sub.1. When
.theta. equals 90.degree., d.theta. is expected to be zero, as the
contact point will simply shift over the boundary without any
rotation of the body. We check this feeling by putting numbers into
Equation 16.
[0080] First of all, notice that according to Equation 17,
d.GAMMA..sub.x/dt=-1 and d.GAMMA..sub.y/dt=0. For .theta.=0,
Equation 16 becomes: d .times. .times. .theta. = .DELTA. .times.
.times. y .times. - 1 ( - t 1 ) .times. ( - 1 ) + 0 0 = - .DELTA.
.times. .times. y t 1 , ##EQU16## which is correct and for
.theta.=90.degree., Equation 16 becomes: d .times. .times. .theta.
= .DELTA. .times. .times. y .times. 0 0 0 + ( - t 1 ) .times. ( - 1
) = 0 , ##EQU17## which is also correct.
[0081] Assume that the body pushes another rod at the boundary in a
point (x.sub.2,y.sub.2), being described by the boundary coordinate
t=t.sub.2. Assume that the rod can move in the x-direction and that
no friction is possible at the contact point in the y-direction.
This results in a movement (.DELTA.x,0). For a given small body
rotation d.theta., the resulting displacement .DELTA.x has to be
found.
[0082] For this displacement, Equation 15 can be rewritten as:
Equation .times. .times. 18 .times. : ##EQU18## .times. { .times.
.DELTA. .times. .times. x = - sin .times. .times. .theta. .GAMMA. x
.function. ( t 2 ) d .times. .times. .theta. + cos .times. .times.
.theta. .times. d .GAMMA. x .function. ( t 2 ) d t .times. d
.times. .times. t - cos .times. .times. .theta. .GAMMA. y
.function. ( t 2 ) d .times. .times. .theta. - sin .times. .times.
.theta. .times. d .GAMMA. y .function. ( t 2 ) d t .times. d
.times. .times. t 0 = cos .times. .times. .theta. .GAMMA. x
.function. ( t 2 ) d .times. .times. .theta. + sin .times. .times.
.theta. .times. d .GAMMA. x .function. ( t 2 ) d t .times. d
.times. .times. t - sin .times. .times. .theta. .GAMMA. y
.function. ( t 2 ) d .times. .times. .theta. + cos .times. .times.
.theta. .times. d .GAMMA. y .function. ( t 2 ) d t .times. d
.times. .times. t ##EQU18.2##
[0083] Eliminating the displacement dt over the boundary gives
.DELTA.x as a function of d.theta.. Equation .times. .times. 19
.times. : ##EQU19## .DELTA. .times. .times. x = - d .times. .times.
.theta. [ ( sin .times. .times. .theta. .GAMMA. x .times. ( t 2 ) +
cos .times. .times. .theta. .GAMMA. x .times. ( t 2 ) ) .times. (
sin .times. .times. .theta. .times. d .GAMMA. x .function. ( t 2 )
d t + cos .times. .times. .theta. .times. d .GAMMA. y .function. (
t 2 ) d t ) + ( cos .times. .times. .theta. .times. d .GAMMA. x
.function. ( t 2 ) d t - sin .times. .times. .theta. .times. d
.GAMMA. y .function. ( t 2 ) d t ) .times. ( cos .times. .times.
.theta. .GAMMA. x .function. ( t 2 ) - sin .times. .times. .theta.
.GAMMA. y .function. ( t 2 ) ) sin .times. .times. .theta. .times.
d .GAMMA. x .function. ( t 2 ) d t + cos .times. .times. .theta.
.times. d .GAMMA. y .function. ( t 2 ) d t ] ##EQU19.2##
[0084] Again, we check the equation with a simple example. Imagine
a boundary defined by: Equation .times. .times. 20 .times. :
##EQU20## .times. ( x y ) .GAMMA. = ( .GAMMA. x .function. ( t )
.GAMMA. y .function. ( t ) ) = ( 0 t ) ##EQU20.2##
[0085] When giving for .theta.=0 a rotation d.theta., the expected
.DELTA.x-displacement is -d.theta.t, which can be found by proper
substitution into Equation 19.
[0086] So far, we found the formulation for an incremental rotation
d.theta. as the result of an imposed displacement .DELTA.y and the
formulation for a load displacement .DELTA.x as the result of an
incremental rotation d.theta. of the body. We take the calculated
value of d.theta. in Equation 16, which gives us the resulting
rotation for an imposed displacement .DELTA.y at t1, and substitute
it in Equation 19 to calculate the displacement .DELTA.x at t2 for
an imposed displacement .DELTA.y at t1. This gives Equation 21.
Equation .times. .times. 21 .times. : ##EQU21## .DELTA. .times.
.times. x = .times. - .DELTA. .times. .times. y .function. [ ( sin
.times. .times. .theta. .GAMMA. x .function. ( t 2 ) + cos .times.
.times. .theta. .GAMMA. y .function. ( t 2 ) ) .times. ( sin
.times. .times. .theta. .times. d .GAMMA. x .function. ( t 2 ) d t
+ cos .times. .times. .theta. .times. d .GAMMA. y .function. ( t 2
) d t ) + ( cos .times. .times. .theta. .times. d .GAMMA. x
.function. ( t 2 ) d t - sin .times. .times. .theta. .times. d
.GAMMA. y .function. ( t 2 ) d t ) .times. ( cos .times. .times.
.theta. .GAMMA. x .function. ( t 2 ) - sin .times. .times. .theta.
.GAMMA. y .function. ( t 2 ) ) ( cos .times. .times. .theta.
.GAMMA. x .function. ( t 1 ) - sin .times. .times. .theta. .GAMMA.
y .function. ( t 1 ) ) .times. ( cos .times. .times. .theta.
.times. d .GAMMA. x .function. ( t 1 ) d t - sin .times. .times.
.theta. .times. d .GAMMA. y .function. ( t 1 ) d t ) + ( sin
.times. .times. .theta. .GAMMA. x .function. ( t 1 ) + cos .times.
.times. .theta. .GAMMA. y .function. ( t 1 ) ) .times. ( sin
.times. .times. .theta. .times. d .GAMMA. x .function. ( t 1 ) d t
+ cos .times. .times. .theta. .times. d .GAMMA. y .function. ( t 1
) d t ) ] .times. cos .times. .times. .theta. .times. d .GAMMA. x
.function. ( t 1 ) d t - sin .times. .times. .theta. .times. d
.GAMMA. y .function. ( t 1 ) d t sin .times. .times. .theta.
.times. d .GAMMA. x .function. ( t 2 ) d t + cos .times. .times.
.theta. .times. d .GAMMA. y .function. ( t 2 ) d t ##EQU21.2##
[0087] When we assume the condition that 0=0 and that the angles of
the body boundary with the contact rods provide normal
(perpendicular) contact points, i.e. ( d .GAMMA. y .function. ( t 1
) d t = 0 , .times. d .GAMMA. x .function. ( t 2 ) d t = 0 ) ,
##EQU22## Equation 21 becomes what we expect in accordance with
Equation 20, i.e. Equation .times. .times. 22 .times. : ##EQU23##
.times. .DELTA. .times. .times. x .DELTA. .times. .times. y = - y 2
x 1 ##EQU23.2##
[0088] Now, let's try to find in a numerical way to describe the
body boundary, i.e. the function (.GAMMA..sub.x,.GAMMA..sub.y), so
that .DELTA.x is a linear function of .DELTA.y. Consider the first
contact point. As the surface around the first contact point is
convex, we can take the following definition for the function
(.GAMMA..sub.x,.GAMMA..sub.y) Equation .times. .times. 23 .times. :
##EQU24## .times. { .GAMMA. x = x .GAMMA. y = y .times. .times. ( x
) ##EQU24.2##
[0089] For deriving the differential equation describing the shape
of the boundary, we take the assumption that the angle in the
contact point with the pushing rod is always zero. If
(.GAMMA..sub.x(t.sub.1).GAMMA..sub.y(t.sub.1)) is the contact
point, then the local slope equals ( d .GAMMA. x .function. ( t 1 )
d t , d .GAMMA. y .function. ( t 1 ) d t ) ##EQU25## and the
corresponding slope at the lever will be, according to the rotation
of equation 14: Equation .times. .times. 24 .times. : ##EQU26##
.times. { S x = cos .times. .times. .theta. .times. d .GAMMA. x
.function. ( t 1 ) d t - sin .times. .times. .theta. .times. d
.GAMMA. y .function. ( t 1 ) d t S y = sin .times. .times. .theta.
.times. d .GAMMA. x .function. ( t 1 ) d t + cos .times. .times.
.theta. .times. d .GAMMA. y .function. ( t 1 ) d t . .times.
##EQU26.2##
[0090] So, for having an ideal contact point pushing against the
lever, we impose the condition that S.sub.y should be zero. Using
the definition of equation 23, the second part of equation 24 can
be written as: Equation .times. .times. 25 .times. : ##EQU27##
.times. 0 = sin .times. .times. .theta. + cos .times. .times.
.theta. d y d x .times. or .times. d y d x = - tg .times. .times.
.theta. ##EQU27.2##
[0091] A second differential equation can be found from the fact
that we want a linear object rotation as a function of the movement
of the pushing rod. The y-movement at the pushing rod is given by
the second term in equation 14, which changes for a elementary
rotation d.theta. as: Equation .times. .times. 26 .times. :
##EQU28## .times. .differential. y .differential. .theta. = cos
.times. .times. .theta. .GAMMA. x + sin .times. .times. .theta.
.times. d .GAMMA. x d t .times. d t d .theta. - sin .times. .times.
.theta. .GAMMA. y + cos .times. .times. .theta. .times. d .GAMMA. y
d t .times. d t d .theta. . ##EQU28.2##
[0092] For .theta. = 0 .times. .times. and .times. .times. d
.GAMMA. y d t = 0 ##EQU29## in the contact point of the pushing rod
with the body, .differential. y .differential. .theta. .times.
equals .times. .times. x 1 . ##EQU30## If we constrain
.differential. y .differential. .theta. ##EQU31## to a constant for
all values of .theta., then this constant value should be x.sub.1!
So, therefore, equation 26 can be written as well: Equation .times.
.times. 27 .times. : ##EQU32## .times. x 1 = cos .times. .times.
.theta. .GAMMA. x + sin .times. .times. .theta. .times. d .GAMMA. x
d t .times. d t d .theta. - sin .times. .times. .theta. .GAMMA. y +
cos .times. .times. .theta. .times. d .GAMMA. y d t .times. d t d
.theta. . ##EQU32.2##
[0093] Using the definition of equation 23, this can be rewritten
as: Equation .times. .times. 28 .times. : ##EQU33## .times. x 1 =
cos .times. .times. .theta. x + sin .times. .times. .theta. .times.
d x d x .times. d x d .theta. - sin .times. .times. .theta. y
.function. ( x ) + cos .times. .times. .theta. .times. d y d x
.times. d x d .theta. . ##EQU33.2##
[0094] Taking also the constraint of equation 25 and putting this
in the above equation gives: x.sub.1=cos .theta.x-sin .theta.y(x).
Equation 29
[0095] This equation in fact says that the x-coordinate of the
contact point should end up at the place x=x.sub.1, which is
actually the first part of equation 14.
[0096] From this algebraic equation 28, d.theta./dx can be found by
differentiating to x: Equation .times. .times. 30 .times. :
##EQU34## .times. d .theta. d x = cos .times. .times. .theta. - sin
.times. .times. .theta. .times. d y d x x .times. .times. sin
.times. .times. .theta. + y .times. .times. cos .times. .times.
.theta. ##EQU34.2##
[0097] Using equation 25, this can be rewritten as: Equation
.times. .times. 31 .times. : ##EQU35## .times. d .theta. d x = 1
cos .times. .times. .theta. ( x .times. .times. sin .times. .times.
.theta. + y .times. .times. cos .times. .times. .theta. )
##EQU35.2##
[0098] We have now a set of differential equations, i.e. equation
25 and equation 31, in the two dependent variables (.theta.,y) with
the independent variable x. This system of first order non-linear
differential equations can be solved numerically, given the
starting position for .theta.=0.
[0099] Commercial software is available for solving this non-linear
system of equations, like e.g. the ode-solvers from Matlab.TM..
[0100] As an example, the contact shapes of a lever have been
calculated by solving equation 25 and equation 31. As an input for
the ode-solver, the following table lists the start positions of
the shape when .theta. equals 0. TABLE-US-00001 TABLE 1 Coordinates
of the initial contact points for a specific lever design. Contact
point 1 Contact point 2 x-coordinate -41.41 2.0 y-coordinate 4
-5.92
[0101] For these boundary conditions, the shape of the contact
zones of the lever has been calculated numerically and depicted in
FIG. 7A and FIG. 7B. FIG. 7A shows the lever contour at the pushing
contact and FIG. 7B shows the contour at the load contact.
[0102] From these calculations, it turns out that there are also
positions for .theta. which form a kind of a singular point. Beyond
this singular point (or .theta.-value), no solution exists and it
is not possible then to have a linear relationship between the y-
and x-displacement. In the example, for the data of Table 1, the
singular angle .theta. for shape 1 equals 5.5.degree. and the
singular angle for shape 2 equals -18.67.degree.. As mentioned
above, a singular angle exists when making a movement into the
negative y-direction, for contact point 1, the y-coordinate of the
contact point becomes zero. Further movement into the negative
y-direction will produce a re-sliding of the contact rod over a
part of the shape, it was sliding over before, for positive
y-values. Therefore, as the rod slides over a same point of contact
for 2 different y-values, it is obvious that the shape can only be
designed for being correct in one y-position, but not in the other
y-position. Therefore, for a good design of the lever, the working
region must be chosen so that one never gets a crossing of the
contact y-coordinate through the y=0 point, thus avoiding the
singular point as illustrated in FIGS. 2A and 2B.
[0103] What about the conversion error from a given y-displacement
in contact point 1 to a resulting x-displacement in contact point
2. Therefore, we numerically evaluate equation 21, and take into
account the ideal situation of equation 22 from which we can define
a factor to measure the relative accuracy of the translations of
the lever as being: Equation .times. .times. 32 .times. : ##EQU36##
.times. .chi. = x 1 y 2 ( .DELTA. .times. .times. x .DELTA. .times.
.times. y ) Eq . .times. 10 ##EQU36.2##
[0104] For a perfect lever operation, .chi. will be identical to 1.
The factor .chi. is depicted for the example lever, according to
Table 1, in FIG. 8. We notice that .chi. is not identical to 1 in
the region between the singular angles [-18.8.degree., 5.5.degree.]
This is because of numerical errors in the calculations. First of
all, small errors are being present because of the numerical
solution of the differential equations. But the greatest numerical
errors will appear from the numerical calculation of equation 21,
where the d{right arrow over (.GAMMA.)}/dt terms are being
estimated numerically as well. So, theoretically, .chi. should be 1
between the 2 singular angles, and become different from 1 outside
the valid .theta.-interval, which can be noticed clearly from FIG.
8 when .theta. passes beyond the 18.8.degree.. In the region from 0
to -20.degree., the maximum movement translation error equals
0.32%. It is stated that errors lower than 0.5% will result in a
substantially linear behavior of the leverage system.
[0105] If we compare these results with a commercial design with
the contact boundaries being approximated by a circle segment,
corresponding .chi. values can be calculated as well and the
resulting transfer factor is depicted in FIG. 9. We notice errors
up to 7%.
B. Kinetics for Contact Points Having Two Degrees of Freedom, but
Limited According to Equation 11
[0106] Instead of redoing the reasoning presented above for the
case where the contact points only have one degree of freedom, the
focus in this sections is only drawn to the differences and
additional points of attentions to come to the boundary of an ideal
lever design with limited 2-dimensional degree of freedom for the
two contact points.
[0107] With reference to the body of FIG. 6 and its coordinate
system, a imposed displacement of (0, .DELTA.y) on the body at
boundary point t=t1 will have a additional displacement component
of the boundary point in the x-direction because A now changes with
the rotation angle .theta. of the body. The addional displacement
component of the boundary point t=t1 equals Adf(.theta.), so that
the displacement of the contact point becomes (Adf(.theta.),
.DELTA.y). In a similar way, the resulting movement of contact
point t=t2 at the body boundary equals (.DELTA.x,-Bdf(.theta.)),
instead of (.DELTA.x,0) for a contact point having only one
dimension of freedom. These considerations will change the
equations 15 and 19 accordingly and will finally ends up with a
relationship between .DELTA.x at t=t2 and .DELTA.y at t=t1
according to equation 33. Equation .times. .times. 33 .times. :
##EQU37## .DELTA. .times. .times. x = - .DELTA. .times. .times. y
.function. [ ( ( sin .times. .times. .theta. .GAMMA. x .function. (
t 2 ) + cos .times. .times. .theta. .GAMMA. y .function. ( t 2 ) )
.times. ( sin .times. .times. .theta. .times. d .GAMMA. x
.function. ( t 2 ) d t + cos .times. .times. .theta. .times. d
.GAMMA. x .function. ( t 2 ) d t ) + ( cos .times. .times. .theta.
.times. d .GAMMA. x .function. ( t 2 ) d t - sin .times. .times.
.theta. .times. d .GAMMA. y .function. ( t 2 ) d t ) .times. ( cos
.times. .times. .theta. .GAMMA. x .function. ( t 2 ) + B .times.
.differential. f .differential. .theta. - sin .times. .times.
.theta. .GAMMA. y .function. ( t 2 ) ) ) ( ( cos .times. .times.
.theta. .GAMMA. x .function. ( t 1 ) - sin .times. .times. .theta.
.GAMMA. y .function. ( t 1 ) ) .times. ( cos .times. .times.
.theta. .times. d .GAMMA. x .function. ( t 1 ) d t - sin .times. d
.GAMMA. y .function. ( t 1 ) d t ) + ( sin .times. .times. .theta.
.GAMMA. x .function. ( t 1 ) + A .times. .differential. f
.differential. .theta. + cos .times. .times. .theta. .GAMMA. y
.function. ( t 1 ) ) .times. ( sin .times. .times. .theta. .times.
d .GAMMA. x d t + cos .times. .times. .theta. .times. d .GAMMA. y
.function. ( t 1 ) d t ) ) ] cos .times. .times. .theta. .times. d
.GAMMA. x .function. ( t 1 ) d t - sin .times. .times. .theta.
.times. d .GAMMA. y .function. ( t 1 ) d t sin .times. .times.
.theta. .times. d .GAMMA. x .function. ( t 2 ) d t + cos .times.
.times. .theta. .times. d .GAMMA. y .function. ( t 2 ) d t
##EQU37.2##
[0108] When we try to find a numerical way to solve this equation,
similar to the way we found a solution in the case with contact
points with only one degree of freedom, we come to a set of
differential equations, equation 34 and 35, in the two dependent
variables (.theta.,y) with independent variable x. Equation .times.
.times. 34 .times. : ##EQU38## .times. 0 = sin .times. .times.
.theta. + cos .times. .times. .theta. d y d x .times. .times. or
.times. .times. d y d x = - tg .times. .times. .theta. ##EQU38.2##
Equation .times. .times. 35 .times. : ##EQU39## .times. d .theta. d
x = 1 cos .times. .times. .theta. ( x 1 .times. d f d .theta. + x
.times. .times. sin .times. .times. .theta. + y .times. .times. cos
.times. .times. .theta. ) ##EQU39.2##
[0109] The function f(.theta.) is known or should be known and is
not a part of the solution. This system of first order of
non-linear differential equations can be solved numerically, given
the starting position for .theta.=0. Commercially, software is
available for solving this non-linear system of equations, like
e.g. the ode-solvers from Matlab.TM..
[0110] As an example, the contact shapes of the body, i.e. the
lever have been calculated by solving equation 34 and 35. As an
input for the ode-solver, the following table lists the start
positions of the shape when .theta. equals 0. TABLE-US-00002 TABLE
2 Coordinates of the initial contact points for a specific lever
design. Contact point 1 Contact point 2 x-coordinate -41.41 2.0
y-coordinate 4 -5.92
[0111] For f(.theta.), we take a linear function, being:
f(.theta.)=1+a.theta..sub.[ ], Equation 36 with a=1 [rad.sup.-1],
in the following numerical example for contact point 1. For contact
point 2, we solve the identical differential equation, but we know
that we have to interchange in the solution x and y, as the contact
surfaces need to ly perpendicular to each other. For the constant a
in equation 32, we have to take a value of -1 [rad.sup.-1] to copy
with this interchange of x- and y-coordinates.
[0112] For these boundary conditions, the contact shape of the
lever has been calculated numerically and are being depicted in
FIGS. 10A and 10B. To our surprise, we notice that the shape in 10B
is convex and it is not so obvious to push with a lever against
this shape. The lever will need a special construction in order to
follow the shape at its back side.
[0113] In both the cases it is clear that the butting surfaces of
the levers are formed by the union of the contact points defined by
the solution of the boundary value problem.
[0114] The main purpose of a lever design according to the
invention is to obtain linearity in the ratio of the movement of
the adjustment means and the movement of the positioning device
relative to a base plate.
[0115] A further object is that the forces acting upon the lever
are always perpendicular to the contact surface and the ratio of
the length of the load arm to the length of the force arms is kept
constant. As described above the working distance D has to be in
between the singular point of the positioning system as described
above.
Practical Embodiment of a Lever Design According to the Invention
in Printhead Positioning Devices
[0116] The defined lever shapes can be put to practice in a
positioning system for printheads, e.g. inkjet printheads.
[0117] Following practical example is given in relation to FIG.
11.
[0118] Referring to FIG. 11 the positioning system used for
positioning a printhead includes features described below. In the
description following the printhead positioning device 10 will be
abbreviated as HPD.
[0119] Fixing of the printing head, not shown, in the HPD 10 and
positioning of the printing head in the Z-direction is realized
using splines fitting in grooves 11. By tightening the screws 12,
13, the associated splines move downward and pushed the printing
head's Z-datum against a base plate 14 which is common for all
printing heads, while at the same time clamping the printing head
into a fixed position within the HPD 10. All printing heads have a
common Z-reference, being the single base plate 14. The base plate
14 has several cut-outs of which one is for receiving the front
side of the printing head, including a nozzle plate with marking
elements, so that the marking elements extend through the base
plate 14.
[0120] The HPD 10 is fixed in the Z direction but can move
relatively to the base plate 14 in the X direction to align the
printing head with a print swath and can rotate with only an
y-translation of the marking elements of the printhead to align the
printing head substantially orthogonal to the printing direction an
indicated by the arrows T and R.
[0121] By use of two anti-play springs 15 and 16 the HPD is pressed
in X and Y direction at one side of other cut-outs in the base
plate so that the edges of these cut-outs in the base plate come in
contact with two dedicated levers 20 and 30.
[0122] The first dedicated lever 20 acts in the Y-direction and can
move the HPD 10 (including the locked printing head) so that the
marking elements of the printing head experience a displacement
that is a function of the position of the marking element in the
array of marking elements and is aimed at rotating the array of
marking elements until an orthogonal position, with respect to the
printing direction, is achieved. The lever 20 contacts the base
plate 14 at contact point 21 and it can be set using adjustment
screw 22 which is coupled to the lever 20 by a intermediate slider
23 contacting the lever at contact point 24.
[0123] By turning the adjustment screw 22 up or down, a movement is
given on the force arm of the first lever 20 via the contact point
24 and the lever 20 rotates around a fixed rotation point on the
HPD frame, pushing the load arm against one side of a cut-out in
the base plate 14 at contact point 21, against the force of the
spring 16. If the HPD 10 were to be fixed to the base plate 14 in a
single point, this single point would be a rotation point of the
HPD 10 (including the locked printing head) as a result of the
force exercised in contact point 21 by lever 20. By rotating, the
array of marking elements not only rotate but also slightly
translate in the X direction. This effect is not desired because
this translation in the X direction interferes with the x-position
adjustment of the printing head using a second dedicated lever, to
be discussed further in this description. One solution to solve
this problem is to have the rotation point of the HPD 10 slide
along the X-axis so that a rotation R is substantially transformed
into a translation along the Y-axis, at least for one marking
element that is used as a reference element in the alignment
process, and the mutual interference between the two position
adjustment means of the HPD is undone. This is illustrated in FIG.
12. The figure clearly shows that a rotation around a translating
rotation point can realize a single non-uniform translation
(different magnitudes) substantially along the Y-axis for a
majority of marking elements, without changing their x-position. In
FIG. 12 rotation point c translates along the x-axis according to
solid arrow 2 while the marking elements ME1 to MEn rotate around
the rotation point c according to solid arrow 1. The combined
rotation 1 and translation 2 results in a translation 3 of the
marking elements that is substantially parallel to the y-axis (see
open arrows on FIG. 12), at least for a reference marking element,
e.g. ME1, that is used in the printing head positioning process to
measure the initial positioning error of the printing head on a
test print. Using the possibility to slide the rotation point, the
position adjustment using lever 20 can be made to not interfere
with the position adjustment using lever 30 discussed further in
this description, provided the proper marking elements are used to
calculate the adjustments based on a test print.
[0124] The second dedicated lever 30 acts in the X-direction and
moves the HPD 10 (including the locked printing head) so that all
marking elements of the printing head experience a uniform
translation (same magnitude) in the X-direction. This adjustment
allows for correctly butting of multiple arrays of marking elements
in the X-direction (i.e. side-by-side). The lever 30 contacts a
side of a cut-out in the base plate 14 at contact point 31 and it
can be set using adjustment screw 32 which is coupled to the lever
30 by a intermediate slider 33 contacting the lever at contact
point 34. By turning the adjustment screw 32 up or down, a movement
is given on the force arm of the second lever 30 via the contact
point 34 and the lever 30 rotates around a fixed rotation point on
the HPD frame, pushing the load arm against the side of the cut-out
in the base plate 14 at contact point 31 against the force of the
spring 15. The HPD 10 is hereby translated as is also the array of
marking elements of the locked printing head as a whole.
[0125] So far, multiple arrays of marking elements may be aligned
parallel to the X-axis and positioned along the x-axis, using the
HPD's described above. The alignment of multiple arrays of marking
elements in de Y-direction is done via electronic control means
(i.e. timing of marking element activation pulses).
[0126] The surface shapes of the contact points 16, 19, 21, 24 of
both dedicated levers 15, 20 comply with the constraints as
described above, needed to obtain linear and thus predictable
displacement of a HPD with reference to precise cut-outs in a base
plate.
[0127] The main advantage of having a proportional relationship
between the driving action of the adjustment means (rotation of a
screw by the operator) and the driven response of the positioning
device (displacement of the printing head relative to the mounting
base plate) is that methods to align printing heads after their
initial position has been detected only requires a few corrective
actions. In a first step the initial position of the printing head
can be detected for example by use of a test print. The test print
can be designed so that position errors are easily deducted or may
be just readable from the print. Matching sets of lines from
different printing heads may indicate directly deviation angles and
distances from ideal placement. First the angular deviation from
parallelism with the x-axis is measured and converted to a
displacement of lever 20 via adjustment screw 22, and secondly the
position error along the x-axis is measured. It may be advantageous
in this position error measuring step to use a reference marking
element of the printing head furthest away from the HPD rotation
point and closest to lever 20 to determine both adjustments. See
also the comments to FIG. 12. When the deviation is known and as
the displacement of the adjustment means is linear it is easy to
perform adjustment of the printing head(s) manually by the
operator. First the array of marking elements can be adjusted
parallel to the x-axis by adjusting the adjustment screw 22. The
required translation along the X-axis can then be performed by
adjustment of screw 32.
[0128] The accessibility of all printing head replacement and
adjustment means at one side of the HPD allows fast and easy
replacement and alignment of a printing head in the event of
malfunction of the printing head. No special service tools or
skills are required to replace and align printing heads; the
procedure can be executed by a printer operator.
[0129] In the depicted embodiment of FIG. 11 the screws are in fact
more a complicated spindle system totally traversing the HPD from
top to bottom. On these spindles the intermediate sliders 23,33 are
mounted and these are moved up or down when turning the spindles
assembly.
[0130] The top to bottom spindles provide the extra advantage that
there is a possibility to adjust the screw/spindle assembly from
the top as well as from the bottom if fitted with e.g. a socket
head ending at both sides.
[0131] This makes that the single design of the head positioning
device can be put to use in more versatile conditions.
[0132] The accessibility of all the alignment and mounting means
from the top and the accessibility of the alignment means from the
bottom helps to keeping maintenance costs low.
[0133] Note that it is important that the actual position
adjustment, i.e. the movement of the "actuators" of the adjustment
mechanisms needs to be located near the front of the printing head
where the marking elements are located. Indeed, the position of the
marking elements is mapped to printed marking points on the
receiving substrate and thus the position of the marking elements,
amongst other aspects, determines the print quality.
[0134] The adjustment screws are preferably of a self-locking
type.
[0135] A possible embodiment uses screws that are equipped with a
locking mechanism in which a small metal sphere is pressed onto a
toothed ring by a small spring. In the depicted embodiment of FIG.
11, the screws have a toothed section 35 which is contacted by a
kind of leaf spring 36 which is cut out in the respective cover
plates closing the side of the HPD.
[0136] As a result of these extra features, a full rotation of the
screw is divided in several clicks. Each time the metal sphere or
leaf spring 36 is pressed into a next tooth of the toothed section
35. This allows for an even better control of the rotation of the
adjustment screw, i.e. each click represents an equal rotation
angle that is transformed by the lever into an equal translation of
the marking elements of the printing head. One of the obvious
advantages of self-locking adjustment means is that the position of
the printing head is secures at all times. Drift of the adjustment
means due to vibrations internal or external to the printer, or
accidental exposure to unwanted influences or forces are
eliminated. Using the system, an incremental small rotation of one
click is first transformed into an even smaller downward movement
of the screw, depending upon the pitch of the thread of the screw,
and is secondly transformed into a minute displacement of the HPD
(including the locked printing head) by using the levers.
[0137] In stead of springs 15, 16 other types of resilient means
can be used to urge the mounting element on the frame or the frame
itself in contact with the lever. Other types may be e.g. resilient
rubber parts.
[0138] As the printing head is fixed in the head positioning device
and the device is adjustably mounted on the base plate, the
mounting features of the printhead can be made simple and cheap.
This makes replacement of a printing head also less expensive.
[0139] The printing head positioning system according to this
invention is suitable for scanning printing systems whereby the
printing heads shuttle back and forth across the width of the
recording medium while the recording medium is transported along
the length direction. However, the printing head positioning system
is also suitable for page wide printing systems whereby the
printing heads are stationary and cover part or the complete width
of the recording medium while the recording medium is transported
in along the length direction. As the head positioning device is
carried on the base plate and may be shuttling back and forth
across the recording medium, preferably the head positioning device
is made of a light material putting less strain on the shuttling
mechanism. Less inertia poses less problems. It should however be
as strong as well to avoid deformation due to the repeating
accelerations as the shuttle starts and stops.
[0140] As can be seen from FIG. 11, in the example the walls of the
head positioning device may be made of a synthetic material having
a grid-like or honeycomb structure having high strength but low
weight.
[0141] It has already been discussed that the preferred location
where the position adjustments of the printing head or HPD are
done, i.e. as close as possible to the marking elements, is not
necessarily the most accessible location for an operator to perform
the adjustments. Therefore the invention provides a way to lead the
access point for the adjustment means away from the adjustment
action itself, via a lever and elongated screw, so as to make
adjustments easily accessible for an operator. The same principle
may also be applied to printing head connections that are required
near the front of the printing head and are difficult to access
once the printing head is mounted in the printing system. One
examples may be a connection of the printing head to a cooling
circuit for cooling the marking elements of the printing head, as
provided near the front of the first generation of XJ500 ink jet
printing head from Xaar plc--Cambridge (UK). Another example may be
the ink connection of XJ128 printing heads from Xaar plc--Cambridge
(UK), that is located on top of the printing head near the front
where the marking elements are located. Still another example may
be the lung mechanism for ink de-aeration incorporated in Galaxy
type printing heads from Spectra Inc--Lebanon N.H. (USA), where the
vacuum connection to the lung mechanism is located near the front
of the printing head. All these connections are difficult to access
once the printing head is mounted in the printing apparatus.
Therefore it may be advantageous to design extension pieces for
these connections into the HPD so as to lead the printing head's
connection point near the front to a side of the HPD that is easily
accessible for making and breaking connections, for example at the
back of the HPD where also the adjustment means for printing head
positioning are located. The connection extension pieces preferably
are provide with proper fittings at the side of the connection with
the printing head so as to seal the hydraulic connection when the
printing head is inserted in the HPD and fixed into the HPD by
means if the splines discussed previously. At the other side of the
connection extension pieces, i.e. the accessible side of the
connection, e.g. at the back of the HPD, any connection type may be
used but an easy operated connection is preferred. The use of lever
systems for positioning of the printing head or HPD with reference
to a base plate and the use connection extension pieces to make
hydraulic connections near the front of the printing head allow all
connections with the printing head, that need to be accessible for
operator intervention, to be diverted to the easiest accessible
side of the HPD.
[0142] Having described in detail preferred embodiments of the
current invention, it will now be apparent to those skilled in the
art that numerous modifications can be made therein without
departing from the scope of the invention as defined in the
appending claims.
* * * * *